hawkeyefan
Legend
I think I would say "System can and often does matter, but it isn't the only thing, and there are ways to solve problems beyond just mechanics or system". I think what sometimes happens though is people see that and they read something more like "System is meaningless" which is far from my position.
I think part of the issue is also what people tend to think of as "the system". Like if the rules say that the GM decides how X comes about, then that's part of the system, I'd say. Others may not agree if there are no game mechanics involved. But I think the division of authority and who gets to decide what and how, falls under "the system".
I think the common element of the games cited in the OP as promoting authenticity is the role of the GM being limited in ways. Ways that don't allow for the methods that are cited as squelching authority. The GM isn't really able to railroad or use the three-clue rule or node-based adventures or predetermine the solutions to problems in those games. They just don't function that way.
I think what also comes into play here, and we've even seen it in this thread, some games are meant to be played in a specific manner, with specific processes in place for the participants to follow. Other games, with D&D notably being among them, have wiggle room in how the processes are applied or how they work. Then you have other games that are almost entirely modular, like GURPS, you use the rules you'd like to build the setting/game you want.
So there's an expectation that games can be altered by whatever means to bridge any difference. And although I think some differences can be bridged, I also think there are some that cannot.